0.1666… as a Fraction

0.1666… (0.16 repeating) as a fraction is 1/6.

How to convert 0.1666… to a fraction

  1. Let x = 0.1666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 16.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 1.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 16 − 1, so 90x = 15.
  5. Solve: x = 15/90. The greatest common divisor is 15, so x = 1/6.

Check

Divide 1 by 6 on a calculator: 1 ÷ 6 = 0.1666666667… which matches 0.1666….

Similar repeating decimals

DecimalFraction
0.151515…5/33
0.153153153…17/111
0.1555…7/45
0.161616…16/99
0.16333…49/300
0.16666…1/6
0.171717…17/99
0.1777…8/45

See also: 1/6 as a decimal.

Another decimal? Browse the repeating decimal to fraction chart, the terminating decimal chart, or use the decimal to fraction converter.